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Nontrivial twisted sums for finite height spaces under Martin’s Axiom

Volume 248 / 2020

Claudia Correa Fundamenta Mathematicae 248 (2020), 195-204 MSC: Primary 46E15, 54G12; Secondary 54D40. DOI: 10.4064/fm609-2-2019 Published online: 29 July 2019

Abstract

We show that if we assume Martin’s Axiom, then there exists a nontrivial twisted sum of $c_0$ and $C(K)$ for every compact space $K$ with finite height and weight at least continuum. This result settles the problem of existence of nontrivial twisted sums of $c_0$ and $C(K)$ for finite height spaces $K$ under Martin’s Axiom.

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